Using the Cosmic Origins Spectrograph onboard the Hubble Space Telescope, we have obtained high-resolution ultraviolet observations of GD 362 and PG 1225-079, two helium-dominated, externally-polluted white dwarfs. We determined or placed useful upper limits on the abundances of two key volatile elements, carbon and sulfur, in both stars; we also constrained the zinc abundance in PG 1225-079. In combination with previous optical data, we find strong evidence that each of these two white dwarfs has accreted a parent body that has evolved beyond primitive nebular condensation. The planetesimal accreted onto GD 362 had a bulk composition roughly similar to that of a mesosiderite meteorite based on a reduced chi-squared comparison with solar system objects; however, additional material is required to fully reproduce the observed mid-infrared spectrum for GD 362. No single meteorite can reproduce the unique abundance pattern observed in PG 1225-079; the best fit model requires a blend of ureilite and mesosiderite material. From a compiled sample of 9 well-studied polluted white dwarfs, we find evidence for both primitive planetesimals, which are a direct product from nebular condensation, as well as beyond-primitive planetesimals, whose final compositions were mainly determined by post-nebular processing.